Edge-wave buckling of rolled elastic strips: asymptotic results

The problem considered in this paper concerns the edge-wave buckling phenomenon commonly encountered in forming processes such as rolling and levelling. Due to the combined action of global tensile forces and residual stresses, the elastic strips involved in these scenarios experience a symmetric short-wave deformation pattern that tends to be confined near their long edges. We use boundary-layer techniques to provide simple estimates for the critical load and the wavelength of the buckling waves. A number of complementary asymptotic features of the marginal stability curves are also reported.

[1]  C. Coman,et al.  Higher-order asymptotics for edge-buckling of pre-stressed thin plates under in-plane bending , 2009 .

[2]  C. Coman,et al.  An asymptotic description of the elastic instability of twisted thin elastic plates , 2008 .

[3]  Hamid Zahrouni,et al.  Buckling and wrinkling during strip conveying in processing lines , 2007 .

[4]  Kazutake Komori,et al.  Analysis of cross and vertical buckling in sheet metal rolling , 1998 .

[5]  Herbert Reismann,et al.  Elastic Plates: Theory and Application , 1988 .

[6]  T. Mura,et al.  Buckling of a rectangular plate under a self-equilibrating stress due to dislocations , 1994 .

[7]  Ciprian D. Coman,et al.  On the wrinkling of a pre-stressed annular thin film in tension , 2007 .

[8]  BUCKLING OF PLATES DUE TO SELF-EQUILIBRATED THERMAL STRESSES , 1985 .

[9]  S. Amelinckx,et al.  The Buckling of a Thin Plate due to the Presence of an Edge Dislocation , 1962, 1962.

[10]  Pierre Montmitonnet,et al.  Hot and cold strip rolling processes , 2006 .

[11]  W. Wieser,et al.  Buckling phenomena related to rolling and levelling of sheet metal , 2000 .

[12]  C. Coman.  Secondary bifurcations and localisation in a three-dimensional buckling model , 2004 .

[13]  J. D. Eshelby,et al.  CXL. Dislocations in thin plates , 1951 .

[14]  The elastic wrinkling of rectangular sheets , 1988 .

[15]  Richard H. Middleton,et al.  The decay of stresses induced by flat rolling of metal strip , 1993 .

[16]  Franz G. Rammerstorfer,et al.  Residual Stress-Induced Center Wave Buckling of Rolled Strip Metal , 2003 .

[17]  Franz G. Rammerstorfer,et al.  Buckling of Free Infinite Strips Under Residual Stresses and Global Tension , 2001 .

[18]  S. Domanti,et al.  Cold rolling of flat metal products: Contribution of mathematical modelling , 1998 .

[19]  C. Coman.  The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips , 2009 .

[20]  Peter Frederic Thomson,et al.  Predicting quarter-buckling and herringbone buckling in rolled strip , 2007 .

[21]  The buckling of a dislocated plate , 1961 .